Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrat...

The perspective-n-point (PnP) problem, which estimates 3D rotation and translation of a calibrated camera from n pairs of known 3D points and corresponding 2D image points, is a classical problem but still fundamental in the computer vision community. It is well studied that the PnP problem can be solved by at least three points [1]. If n ≥ 4, the PnP problem becomes a nonlinear problem where t...

In this paper mixed finite element methods of higher-order for time-dependent contact problems are discussed. The mixed methods are based on resolving the contact conditions by the introduction of Lagrange multipliers. Dynamic Signorini problems with and without friction are considered involving thermomechanical and rolling contact. Rothe’s method is used to provide a suitable time and space di...

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely obstacle problem. Since adopt a numerical point of view, first relax feasible domain problem, then using both mathematical programming methods penalization get optimality conditions with smooth Lagrange multipliers. Some experimen...

and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...

Time-series predictions by artificial neural networks (ANNs) are traditionally formulated as unconstrained optimization problems. As an unconstrained formulation provides little guidance on search directions when a search gets stuck in a poor local minimum, we have proposed to use a constrained formulation in order to use constraint violations to provide additional guidance. In this paper, we f...

Time-series predictions by artificial neural networks (ANNs) are traditionally formulated as unconstrained optimization problems. As an unconstrained formulation provides little guidance on search directions when a search gets stuck in a poor local minimum, we have proposed recently to use a constrained formulation in order to use constraint violations to provide additional guidance. In this pa...

In this paper we investigate how to efficiently apply ApproximateKarush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model to...